Using a stand mixer fitted with the paddle attachment, mix together the flour, baking powder, baking soda, salt, sugar, ground ginger, crystallized ginger, and lemon zest on low speed for 10-15 seconds, or until combined. Scatter the butter over the top and beat on low speed for about 30 seconds, or until the butter is somewhat broken down and grape-size pieces are still visible.

In a small bowl, whisk together the buttermilk, cream, egg, and grated ginger until thoroughly mixed. On low speed, pour the buttermilk mixture into the flour-butter mixture and beat for 20-30 seconds, or just until the dough comes together. There will still be a little loose flour mixture at the bottom of the bowl.

Remove the bowl from the mixer stand. Gather and lift the dough in your hands and turn it over in the bowl, so that it starts to pick up the loose flour at the bottom. Turn the dough over several times until all of the loose flour is mixed in.

Dump the dough onto a lightly floured work surface and gently roll it out about 1 inch thick. Using a 3 1/2-inch round cookie cutter, cut out circles. (At this point, the unbaked scones can be frozen, tightly wrapped in plastic wrap, for up to 1 week. Proceed as directed, baking directly from the freezer and adding 5 minutes to the baking time.) Place them on a baking sheet, spacing them 2-3 inches apart.

Bake at 350 for 15 minutes, or until the scones are a light golden brown on top. Transfer to a wire rack to cool for 10-15 minutes.

To make the lemon glaze:

While the scones are cooling, in a small bowl, whisk together the powdered sugar and enough of the lemon juice to make a smooth, thick, pourable glaze. You should have about 1/2 cup.

When the scones have cooled for 10-15 minutes, brush the tops evenly with the lemon glaze.